Apparatus and method for accurate energy device state-of-health (SoH) monitoring

ABSTRACT

A device and associated testing method for testing state of health of an energy device, comprising: applying electrical excitations to the energy device at a predetermined electrical excitation frequency ω e ; applying mechanical excitations to the energy device at a predetermined mechanical excitation frequency ω m ; measuring an electrically-induced phase difference Δθ e  (ω e ) between voltage (V) and current (I) within the energy device from applying the electrical excitations; measuring a mechanically-induced phase difference Δθ e  (ω m ) between voltage (V) and current (I) within the energy device from applying the mechanical excitations; and deducing the state-of-health of the energy device by comparing the electrically-induced phase difference Δθ e  (ω e ) with the mechanically-induced phase difference Δθ e  (ω m ).

BACKGROUND OF THE INVENTION

Electrochemical impedance spectroscopy (EIS) has been used in studies ofelectrode and plate behavior during charging and discharging for years.The impedance response of the battery, or more broadly, anyelectrochemical energy storage and/or conversion device (includingcertain types of fuel cell technologies, solar cells, and even certaintypes of capacitor technologies), depends on the measurement frequencyand the “state” of the energy device at the time it is tested. For thespecific case of a battery, this method has been reported to beaffected, to varying degrees, by many fundamental battery parameters,including battery design, manufacturing tolerances, aging, temperature,and state-of-charge (SoC). The goal of EIS State-of-Health (SoH)monitoring techniques is to extract as much information as possibleabout the electrochemical health of the battery. Based on thevariability introduced by the parameters noted above this monitoringtechnique has fallen short in the market place. The evolution of thetechnology followed a very predictable path and this applicationdiscloses the next generation of this technology which is arevolutionary break-through in the science of EIS SoH batterymonitoring.

This disclosure will elucidate the novelty, inventive step andindustrial viability of a method and device for more accuratelymeasuring the SoH of an energy device by illustrating the drawbacks ofthe current SoH measurement and prediction techniques on lead acidbattery chemistry, and showing how using ultrasonic energy as part ofthe measurement process overcomes these deficiencies. However, it shouldbe understood that the disclosures here can be applied to anyelectrochemical energy storage and/or energy conversion devices(generally referred to simple as “energy devices”), including but notlimited to, certain types of fuel cells, solar cells and capacitortechnologies. In the broad understanding of the method and devicedisclosed here, it applies to any electrochemical energy device in whichthere are ionic species kinetic limitations and/or deficiencies. Certainfuel cells, solar cells and capacitors also have known ionic kineticdeficiencies which impact their operating characteristics andperformance and it should be understood that this method and devicedisclosed encompasses these type of devices as well.

A brief background is necessary in order to elucidate the novelty of theinvention being presented. In recent years there has been considerableactivity and debate regarding the use of internal “impedance”characteristics as a battery condition measurement. The interestreflects the desire for simple electronic means to replace dischargetesting as a practical determination of residual battery capacity,particularly given the increased usage of valve-regulated lead-acid(VRLA) batteries (for the lead acid chemistry example). It is widelyaccepted that the only way to truly know the true health of a battery isto periodically conduct test discharges. Once the test discharge iscomplete, and passes, this is a ‘good’ indicator that the battery isoperating as designed and it provides peace-of-mind that the batterywill perform its intended function when called upon. Unfortunately,conducting a test discharge is costly and time consuming. Moreimportantly, if a test discharge is run on a battery pack too often itwill ultimately reduce the battery's operating life, and the subsequentreplacement will prove to be extremely costly. Batteries do not respondwell to being fully discharged and it directly takes away from thebattery life.

When conducting a test discharge it is often necessary to take thebattery off-line, i.e. disconnect from its intended function, andtherefore alternative measures for back-up power need to be in place.Typically, a back-up battery pack, or other means of power, such asdiesel generator, fuel-cell, etc., is added to the system design tominimize the impact of this necessary operational restriction, however,this brute force attempt adds significant up front capital andmaintenance cost to the project. The length of a test discharge for aprimary battery back-up plant is dependent on the rate at which it isdischarged. Typically, this time is determined by how much of a load ison the system and how long it may be needed in an emergency situation.As a point of reference, some applications require the battery pack tosupport critical loads for a period up to ˜72 Hours. Therefore, theminimum time the battery pack will be off-line is approximately 3 days,while the battery is being discharged. However, after the 3-day testdischarge is complete the battery is still not available for itsintended function. The battery must be charged back up and this is alsoa time consuming process. If the battery is charged too hard or too fastit will take away from the battery's operating life, and again thereplacement costs are significant. Thus, a general rule is that thebattery should be charged for at least the length of time it wasdischarged, however, battery manufacturers would prefer a much longercharge time (on the order of 30 days for very large lead-acid batterypacks). Therefore, the minimum time the critical battery back-up sourcein this example will be off-line, excluding set-up and testing time, isapproximately 6 days. However, this aggressive charging algorithm is onthe edge of what battery manufacturers are willing to warrantee, soprudent engineering judgment would dictate using longer charge times,thus increasing the down time of a critical energy source.

A purpose of this novel, inventive and industrious mechanical excitationtechnique is to remove this inherent uncertainty in the electronicmeasurement technique, thereby obviating the need to conduct frequentand costly test discharges. Conducting periodic test discharges of theplants critical battery back-up not only places sever operationalrestrictions on the plant, but, even more importantly it reduces theoperating life of the battery pack and results in premature battery packreplacement. If the utility tries to minimize the length of time thatthis necessary operational restriction is in place, by charging thebattery at a faster than recommended rate, than this will ultimatelyresult in unwanted and premature costly battery pack replacement. Thus,the peace of mind that comes with knowing that your critical batteryback-up source is ready for its intended function comes at a great cost.The utility has to weigh the risk of minimizing operational restrictionsagainst the looming cost of replacing its battery pack. As a result,many companies are attempting to determine the battery health withouttest discharging. The method disclosed herein will offer a piece of mindto the plant owners that there battery pack will perform its intendedfunction without the need to perform costly, restrictive and timely testdischarges.

SUMMARY OF THE INVENTION

A device and associated testing method for testing the State-of-Health(SoH) of an electrochemical energy storage and/or energy conversiondevice (“energy device”) and ascertaining addition electrochemicalhealth information that would not be available without said method,comprising: applying electrical excitations to the energy device at apredetermined electrical excitation frequency ω_(e); applying mechanicalexcitations to the energy device at a predetermined mechanicalexcitation frequency ω_(m); measuring an electrically-induced phasedifference Δθ_(e) (ω_(m)) between voltage (V) and current (I) within theenergy device from applying the electrical excitations; measuring amechanically-induced phase difference Δθ_(e) (ω_(m)) between voltage (V)and current (I) within the energy device from applying the mechanicalexcitations; and deducing the state-of-health of the energy device bycomparing the electrically-induced phase difference Δθ_(e) (ω_(e)) withthe mechanically-induced phase difference Δθ_(e) (ω_(m)).

This same method can be used to provide accurate run-time and electricalperformance information and life time predictions for the energy device.In one embodiment of the invention, one applies this testing method anddetermines a baseline phase difference between current and voltage.Then, at a later time, when it is desired to test the health of theenergy device, one again applies this testing method and compares thelater phase difference with the baseline phase difference. The laterphase difference diminishing from the baseline phase differenceindicates energy device aging, and a decline in the energy device'selectrochemical health, roughly linearly with the diminution. Usingvarious prediction algorithms' and prediction techniques this method anddevice can be used to accurately predict the energy devices residualenergy capacity available for use as well as the devices remaining lifetime.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the invention believed to be novel are set forth in theappended claims. The invention, however, together with further objectsand advantages thereof, may best be understood by reference to thefollowing description taken in conjunction with the accompanyingdrawing(s) summarized below.

FIG. 1 is a graph illustrating the phase relationship between voltage(V) and current (I) in an ideal capacitor.

FIG. 2 illustrates a model of a flooded type lead-acid battery.

FIG. 3 is a graph illustrating the phase relationship between voltage(V) and current (I) using a single-frequency EIS technique.

FIG. 4 is a graph illustrating the phase relationship between voltage(V) and current (I) using a dual-frequency EIS technique.

FIG. 5 is a graph illustrating the phase relationship between voltage(V) and current (I) using an ultrasonic technique.

FIG. 6 is a graph illustrating in general terms, true state of healthmeasurement in accordance with various embodiments of the inventionbased on voltage (V) versus current (I) phase differences usingelectrical and mechanical excitations.

DETAILED DESCRIPTION

This disclosure will elucidate the novelty, inventive step andindustrial viability of this method and device by illustrating thedrawbacks of current SoH measurement techniques on lead acid batterychemistry, however, it should be understood that this technique can beapplied to any electrochemical energy storage and/or conversion device;including, certain types of fuel cells, solar cells and capacitors (i.e.hybrid and super capacitor technologies).

In general, many of the inherent limitations of typical electrochemicalenergy storage and/or conversion devices are the result of kineticdeficiencies, i.e. low diffusion and migration rates of the chemicalreaction product ions (i.e., ionic species). In fact, these same kineticdeficiencies are the main differentiator between the performance of anideal capacitor and an electrochemical energy storage device (e.g.,battery). Certain types of fuel cells, such as: Polymer ElectrolyteMembrane (PEM) also have ionic kinetic deficiencies for which thismethod and device can be exploited to gain additional electrochemicalhealth information which will help provide accurate SoH measurement andprediction methods. In an ideal capacitor there is no chemical reactiontaking place and therefore the ionic species kinetic transportlimitations are non-existent and do not impact this storage device'sperformance, i.e. almost instantaneous charge time and almost infinitecycle life. However, ideal capacitors do not have the energy storagecapability that would be useful for large critical energy storageback-up applications. In fact, their storage capacities are orders ofmagnitudes less than that of even the most limited electrochemicalstorage device (e.g., battery). There are other types of capacitors onthe market and in development in which there are chemical reactionstaking place and which therefore suffer from ionic kinetic limitations,however; in this disclosure we will utilize the behavior of this idealcapacitor as an example, without implied limitation, to elucidate theeffectiveness of the disclosed novel and innovative EIS SoH monitoringmethod and device.

The Phase Relationship Between Voltage (V) and Current (I) Across anIdeal Capacitor

FIG. 1 is a phase diagram that will be used throughout the remainder ofthis disclosure to provide insight into the novelty and inventiveness ofthis method and device. In this disclosure the use of the term ‘ideal’in reference to the ideal capacitor is used to elucidate the lack ofionic kinetic deficiencies that plague many other types ofelectrochemical energy storage and/or energy conversion devices. In thisdiagram the phase relationship between Voltage (V) and Current (I) whenapplied to an ideal capacitor is depicted. A very small amplitudesinusoidal voltage is applied across the terminals of the capacitor andthe resultant phase difference (Δθ) of the current response is measured.In the case of an ideal capacitor this Δθ difference is exactly 90°. Onemay ask that if we applied V first then why does the current (I) show upfirst in the phase diagram. This is not intuitive, so it will bediscussed briefly. When the electric potential is felt across thecapacitor electrodes, electrons start to accumulate on the negativeelectrode and then they essentially push electrons off the positiveelectrode, thus leaving that electrode positively charged, and this iswhen the V across the capacitor electrodes begins to grow. So, when allthe electron flow stops (point A in FIG. 1), the maximum V is measuredacross the capacitor terminals.

The phase relationship depicted in FIG. 1 is that of an ideal capacitor.The only charge carriers involved are electrons and there are nochemical reactions happening within that capacitor and therefore thereare no ionic kinetic limitations or deficiencies. Clearly, if this sameV signal was applied across the terminals of a battery, anelectrochemical device which does undergo chemical reaction steps, thephase difference Δθ between V and I will be very different. This newphase difference will be a result of many factors, but, the mostsignificant difference will be due to the introduction of a new type ofcharge carrier, the chemical product ion charge carriers. These ioncharge carriers are much slower than electrons and their rates aredependent on many different factors which will be discussed below.

The Single Electrical Excitation Frequency (ω_(e)) Technique

Early attempts at determining the health of a battery without invokingdisruptive and costly test discharges fell short. With this technique, asmall sinusoidal electrical excitation voltage is applied across thebattery's terminal and the resultant phase difference Δθ of the responsecurrent is measured. The clear advantage of this method is that it canbe used without taking the critical battery back-up off-line and it is avery fast test. If this method of SoH determination was accurate then itwould obviate the need to take the battery pack out of service, and itwould eliminate the resultant operational restrictions discussed above.The phase difference Δθ is correlated to the battery's internalimpedance (Z_(INT)), thus it is an indirect measure of the battery'sopposition to the flow of energy and this can be related to the healthof the battery. In order to examine this technique closer a typical andaccepted model of a flooded type lead-acid battery which will be usedand it is depicted in FIG. 2, where:

-   -   R_(m)=Metallic Resistance (post, alloy, grid, and gridpaste)    -   R_(el)=Electrochemical Resistance (paste, seperator, and        electrolyte)

In FIG. 2, the top depiction models the physical components that offeran opposition to the flow of energy through the battery. The equivalentcircuit (the bottom depiction) has grouped these components in order tobetter describe the battery's behavior as it relates to different typesof charge carriers (i.e. ions and electrons). The capacitance symbol(C_(b)) represents the storage capacity of the battery. The metallicresistance (R_(m)) represents the opposition to the flow to electroncharge carriers, and the electrochemical resistance (R_(el)) representsthe opposition to the flow of ion charge carriers. This breakout ofcharge carrier oppositions will aid in the following description:

-   -   (1) Complex Impedance of Battery (Z_(INT))

$Z_{INT} = {\left( {{R_{m}\left( \omega_{e} \right)} + \frac{\frac{1}{R_{el}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}}} \right) - {j\left( \frac{\omega_{e}{C_{b}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{1}} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} \right)}}$

where;

-   -   C_(b)=Battery Capacitance        ω_(e)=electrical excitation Frequency

Equation 1 above was derived by performing a simple AC analysis of theequivalent circuit in FIG. 2. Z_(int) is an expression for the totalcomplex impedance of the battery, which represents the opposition to theflow of energy to an AC electrical excitation signal with a frequency(ω_(e)). As a note: If a DC signal is applied, then ω_(e)=0, and theZ_(int) expression simplifies to Z_(int)=R_(m)+R_(el).

-   -   (2) Voltage (V) and Current (I) phasor relationship

$\frac{V\left. \sqrt{}\theta_{e} \right.}{I} = Z_{INT}$

Where;

-   -   θ_(e)=Phase Angle due to electrical frequency excitation

Equation 2 above is an expression of the phase relationship between V, Iand Z_(INT). This is merely Ohm's Law rearranged and in its complexform. The resultant phase angle (θ_(e)) is presented with sub-script(e), and this is associated with the electrical excitation frequency(ω_(e)) presented in Equation (1). These subscripts are not typicallyshown, but this granularity will be useful in demonstrating the noveltyof the method being disclosed.

As shown in Equations (2), the phase angle (θ_(e)) can be correlated toZ_(INT). It should be recognized that if Z_(NT) changes its response toan AC excitation signal, for any reason, then its resultant compleximpedance response, at a certain frequency (ω_(e)), will change as welland will result in a different phase angle (θ_(e)). If it is assumedthat the V, I and ω_(e) between various measurements are the same, thenthe resultant phase angle (θ_(e)), the measured parameter, will bedependent on Z_(INT) only. Thus, the phase angle response between V andI at a specific frequency (ω_(e)) can be correlated to the compleximpedance Z_(INT) of a battery at the time the measurement is taken andin theory can be used to indirectly determine the health of a battery.However, in practice, this method is far from accurate as will bediscussed later in this disclosure.

The Battery's Complex Impedance Z_(INT)

As the battery ages the available active material (energy capacity-Ahrs)decreases, lead sulfate and other tertiary compounds crystallize andform unwanted bonds, causing non-rechargeable masses to form on, aroundand within the electrode paste, the charge acceptance declines, thecyclic efficiency falls off, the power density declines, and eventuallythe battery cannot serve its intended function. Each of the componentsin FIG. 2 are effected by battery aging phenomenon in a different wayand each of their contributions will impact the battery's compleximpedance (Z_(INT)) in a different way. This will show up in adifference in the measured phase angle (θ_(e)) between the V and I at aspecific frequency (ω_(e)). In Equation 1 above, it is clear that R_(m),R_(el), C_(b) and ω_(e) all affect the complex impedance response to anelectrical excitation signal.

In addition to aging phenomenon, there other battery conditions thatalso affect the complex impedance response of the battery, such as; theState-of-Charge (SoC), the battery's internal Temperature (T), thebattery design, and the battery manufacturing tolerances and process.These conditions affect the battery components, and their contributionto Z_(INT), and this also results in a difference in the measured phaseangle (θ_(e)). A closer look into how each of these components areaffected by these factors is necessary in order to better understand theproblems with the accuracy of the single frequency excitation measuringtechnique. The key to understanding the limitations on the accuracywhich is possible with the single frequency excitation method is tounderstand the variability that is introduced into this measurementtechnique by the different components in the battery model depicted inFIG. 2. Each of these components are impacted differently by thebattery's age, SoC, temperature and its design (material andconstruction), manufacturing and process tolerances. In order for thistechnique to be an accurate and trusted SoH monitor it must revealinformation about the true electrochemical health of the battery. Itsmeasurement result cannot be altered by battery conditions such as SoC,temperature and its design or it will not supply the proper informationto the battery user in order for them to make critical and costlydecisions about their battery pack.

How does battery aging affect Z_(INT)?

In general, R_(post), R_(alloy) and R_(grid), which are all componentsof R_(m), are not significantly impacted by battery aging. However, thefollowing components are affected:

-   -   a) RGridpaste, a component of R_(m). During the first several        cycles of a lead acid battery the bonding between the grid and        paste tends to get stronger, after that, the bonds tend to break        down. Thus, the contribution of this component to the resultant        phase angle (θ_(e)) will cause it to go one way at the beginning        of life and then go the other way as the battery ages, further        adding to the variability of this type of measurement technique.    -   b) R_(paste), a component of R_(el), increases as the battery        ages and this is mainly a result of unwanted tertiary compounds,        i.e. lead oxides and basic lead sulfates (tribasic and        tetrabasic), precipitating out of solution in unbalanced        alkalinity conditions during the discharge. These tertiary        compounds interact and establish bonding relationships with the        rechargeable PbSO₄ volume and the electrode, on the surface of        the electrode and within its pores. These interactions (i.e.        bonds) are mainly of the covalent or even metallic type, but        regardless of the type, they are undesired because they        negatively impact the storage device's capacity. This        effectively limits the flow and subsequent ionic transfer of the        electrolyte's chemical ion products and presents itself as an        increase to the opposition of the flow of energy, that is, an        increase in Z_(INT). This is essentially a decrease in the        active material utilization (measure of the battery's        capacity-Ahrs). One can see how this negatively impacts both the        discharge and charge of the battery. During discharge there is        less active material available to undergo energy conversion, and        during recharge any additional compounds and/or bonding that is        created during the discharge reaction must be undone during the        recharge reaction (i.e., decrease in charge acceptance). The        resultant contribution of this component tends to increase the        phase angle (θ_(e)) as the battery ages thus further adding to        the variability of this measurement technique.    -   c) R_(sep), a component of R_(el), tends to break down as the        battery ages and this also affects the resultant phase angle        (θ_(e)), thus further adding to the variability of this        measurement technique.    -   d) R_(electrolyte), a component of R_(el), is rather complicated        since there are so many different types of electrolytes        currently used in the industry: Liquid, Gel, and Absorbent Glass        Matting (AGM), etc. The list is large and the aging mechanism of        each is different, some worst then others; however, in general,        the contribution of this component to the resultant phase angle        (θ_(e)) will be affected by battery age thus further adding to        the variability of this type of measurement technique.    -   e) C_(b), a component of the battery model in FIG. 2 is also        affected by aging. Since C_(b) is a measure of the battery's        internal capacitance the same aging effects described for        R_(paste) and R_(Electrolyte) also affect the battery's capacity        to supply energy. Generally the variability of the measurement        technique due to this component increases as the battery ages.        How does Battery State-of-Charge (SoC) Affect Z_(INT)?

In general, R_(post), R_(alloy), R_(grid), R_(gridpaste), which are allcomponents of R_(m), and R_(sep), components of R_(el), are notsignificantly impacted by the battery's SoC. The following componentsare affected:

-   -   a) R_(electrolyte), a component of R_(el), is highly dependent        on the battery's SoC. The opposition to the flow of energy, i.e.        ions, increases as the concentration of the SO₄ ⁻⁻ in the        electrolyte solution goes down. Effectively, there are less SO₄        ⁻⁻ to react with the active material ions (Pb⁺⁺) and this        presents itself as an increase to the opposition of flow.        Therefore, the contribution of this battery condition will        change the resultant phase angle (θ_(e)), thus, further adding        to the variability of this measurement technique. This        variability also increases as the battery discharge continues.    -   b) R_(paste), a component of R_(el), is dependent on the        battery's SoC. If the battery cell is not fully charged than        there is lead sulfate layer on the surface and within the pores        of the plate. Thus, this layer increases the opposition to the        flow of ions. Therefore, the contribution of this battery        condition will change the resultant phase angle (θ_(e)), thus        further adding to the variability of this measurement technique.        This component of R_(el) is also the component that causes the        battery's terminal voltage to go down when the battery reaches        very low SoC. During the first major portion of the discharge of        a lead acid battery the output voltage is relatively constant,        however, near the end of discharge the voltage rapidly        decreases. As Z_(INT) rapidly increases this marks the end of        discharge. Thus, the contribution of this battery condition will        also change the resultant phase angle (θ_(e)) and the        variability of this measurement technique will increase as the        discharge continues    -   c) C_(b), a component of the battery model in FIG. 2 is also        affected by SoC. If the battery cell is not fully charged than        there is lead sulfate layer on the surface and within the pores        of the plate. Thus, this layer alters the permittivity of the        cell thus affecting the representative capacitance of the cell.        Therefore, the contribution of this battery condition will        change the resultant phase angle (θ_(e)), thus further adding to        the variability of this measurement technique.        How does Battery Temperature Affect Z_(INT)?

In general, R_(Sep), a component of R_(el), could be temperaturesensitive, but, in general it is not over the temperature ranges ofinterest, therefore in most practical situations this component willhave minimal impact on the resultant phase angle (θ_(e)). The effects ofthe contribution of temperature on C_(b) is minimal compared to theeffects noted below. The following components are affected bytemperature:

-   -   a) R_(Grid), R_(Alloy), R_(post), and R_(Gridpaste), components        of R_(m), are temperature sensitive. Therefore, a majority of        the metallic opposition (R_(m)) to the flow of energy, i.e.        electron flow, depends of the battery's temperature when the        measurement is taken. Thus, this battery condition affects the        contribution that these components add to the resultant phase        angle (θ_(e)), further adding to the variability of this        measurement technique.    -   b) R_(electrolyte), and R_(paste), components of R_(el), are        highly sensitive to temperature. Anytime one heats up a chemical        reaction the reaction rate will increase. Thus, this battery        condition affects the contribution that these components add to        the resultant phase angle (θ_(e)), further adding to the        variability of this measurement technique.        How do Battery Design, and/or Manufacturing Tolerances and        Process Affect Z_(INT)?

In general, all the components of the battery are affected by itsdesign/manufacturing tolerances and process. However, some are not assignificant as others.

-   -   a) The components of R_(m) are subject to variations based on        different battery designs and the materials used. More        importantly, these components are highly susceptible to        manufacturing tolerances and processes, i.e. various        welding/bonding techniques. Each manufacturer makes the battery        slightly different, therefore the complex impedance response for        the same battery chemistry will be different. Just because all        the batteries are of the same lot does not mean their electrical        response characteristics are the same. Manufacturing batteries        is a messy and highly variable process. Particularly, every        battery will have its own impedance signature, thus affecting        the resultant phase angle (θ_(e)) and further adding to the        variability of this measurement technique.    -   b) The paste, separator and electrolyte are tightly controlled        via industry regulations. R_(paste), R_(sep) and        R_(electrolyte), components of R_(el), and are less susceptible        to design, manufacturing tolerances and/or process variations.        Nonetheless, the complex impedance response and thus the        resultant phase angle (θ_(e)) are affected by this factor, thus,        adding to the variability of this measurement technique.    -   c) Clearly C_(b) is very dependent on the design and        manufacturing process and therefore this battery condition        affects the contribution that this component adds to the        resultant phase angle (θ_(e)), further adding to the variability        of this measurement technique.

It is worth noting that since each battery is a bit different, i.e. hasa different electrical excitation frequency response, the actual EISequipment that different manufacturers design also add to thevariability of this measurement technique. So even a battery from thesame lot and under tight industry regulation will respond differentlyand different conclusions will be drawn on the health of the battery,based on the resultant phase angle (θ_(e)), because the EIS manufactureruses a different electrical excitation frequency. Manufacturers have notsettled on the same (the right) electrical excitation frequency and thisalone adds variability to this measurement technique.

In summary, the single frequency measurement technique comes withsignificant measurement variability and this takes away from itsaccuracy. Therefore, any results from this technique will remain inquestion and its ability to eliminate the costly, restrictive and timeconsuming test discharge has fallen short. At best, this technique maybe useful in identifying imminent failure, i.e. a rogue cell, but thisis too little, too late. Consequently, based on the inherent variabilityin this measurement technique, if it were the only indicator the utilityused in determining the health of a battery pack then costly ‘premature’battery pack replacement would be likely based on uncertainty alone.

FIG. 3 shows the resultant phase angle (θ_(e)) using the singleexcitation frequency EIS technique. The green shaded area isrepresentative of the phase difference from that an ideal capacitorwould present at the same frequency (recall from FIG. 1 that for anideal capacitor V reaches a maximum or minimum just as I is zero, andvice versa). The difference is based on the battery's inherent kinetictransport limitations, i.e. slower ion flow, but, it is also comprisedof the variability and uncertainly that was a result of the change inthe battery's complex impedance response from the effects of aging, SoC,temperature, and battery design, manufacturing tolerances and/orprocesses. Therefore, it should be clear that only part of the greenshaded area truly represents the battery's SoH, it's age, and the restrepresents inherent features of the battery even for a brand new batterywith excellent SoH.

One could surmise that each of the EIS equipment suppliers coulddetermine the complex impedance response of each and every battery thatis available and use this beginning of life measurement to yield betterresults. This equipment manufacturer could keep an extensive database sowhen their equipment was used it would give a better indication of thatbattery's health. However, this is a daunting task to say the least;first battery manufacturers are not that forthcoming with battery dataand they would most likely not provide this initial measurement,secondly there are way too many types of batteries available to keeptrack of, and finally this would only remove some of the variability'sdiscussed above. Therefore, this attempt would significantly complicateand add cost to this measurement technique and the benefits forundertaking this approach would be obviated by the remaining variability(inaccuracy) that was still in the measurement.

True State-of Health (SoH) Meaning

SoH has many different meanings and is often misinterpreted. True SoHmeasurement is supposed to give the user a better understanding of thechemical potential energy (Joules) that is available for conversion touseable electrical energy (Ahrs) when the battery is called upon. If themeasurement technique used is influenced by factors such as SoC,temperature, and battery design, manufacturing tolerances and/orprocess, as is the single frequency excitation technique, then the userwill not be presented with the right information to make a decisionwhether or not to replace the battery pack. This uncertainty is costlyto say the least and thus this is why utility companies still to thisday rely on costly, restrictive, and time consuming periodic testdischarges.

What we really want to know from a SoH measuring technique is thebattery pack's true electrochemical health. The SoC, temperature andbattery design, manufacturing tolerances and/or process, and theircontributions to the battery's complex impedance response, and resultantphase angle response, does not tell us whether or not our battery packis healthy and we need a way to factor these out. What we really need toknow in order to make an informed decision about our battery's health ishow old is it, the battery's age in electrical terms! Clearly, we wantto know how our battery pack has aged based on the regimen we have putit through. So, in order for a measuring technique to be informative weneed to eliminate the variability that is introduced by its componentsbased on SoC, temperature, and battery design, manufacturing tolerancesand processes and we also need to eliminate the variability introduce bydifferent EIS measuring equipment. As discussed previously, each EISdevice manufacturer uses different electrical excitation frequencies andthis alone introduces measurement variability. If one could get all themanufactures to use the same electrical excitation frequencies then thisvariability could be substantially reduced, but this is highly unlikely.The resultant measurement needs to tell us about how the age of thebattery is going to impact its ability to serve its intended functionwhen called upon, Joules to AHrs conversion. Thus, the measuringtechnique needs to somehow eliminate the variability's discussed above.

From FIG. 3, the ultimate goal is to reduce the green shaded area, whichwould mean that some of the variability introduced by factors other thanbattery aging would have to be eliminated and the resultant measurementwould be more indicative of the battery's true SoH, i.e. itselectrochemical health.

Dual Electrical Excitation Frequency (ω_(e) ¹ and ω_(e) ²) Attempt

As a natural response to the shortcomings of the single frequencymeasurement method, an attempt was made to use two electrical excitationfrequencies, ω_(e) ¹ and ω_(e) ² respectively. The goal here was toextract additional electrochemical health information, by eliminatingsome of the variations introduced by non-relevant factors, by excitingthe battery with two different electrical excitation frequencies, closein time. However, this method also fell short. The followingrelationships illustrate this concept:

-   -   (3) Complex Impedance of Battery (Z_(INT)), with ω_(e) ¹ and        ω_(e) ²

$Z_{INT}^{1} = {\left( {{R_{m}\left( \omega_{e}^{1} \right)} + \frac{\frac{1}{R_{el}\left( \omega_{e}^{1} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{1} \right)} + \left( {\omega_{e}^{1}{C_{b}\left( \omega_{e}^{1} \right)}} \right)^{2}}} \right) - {j\left( \frac{\omega_{e}^{1}{C_{b}\left( \omega_{e}^{1} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{1} \right)} + \left( {\omega_{e}^{1}{C_{b}\left( \omega_{e}^{1} \right)}} \right)^{2}} \right)}}$$Z_{INT}^{2} = {\left( {{R_{m}\left( \omega_{e}^{2} \right)} + \frac{\frac{1}{R_{el}\left( \omega_{e}^{2} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{2} \right)} + \left( {\omega_{e}^{2}{C_{b}\left( \omega_{e}^{2} \right)}} \right)^{2}}} \right) - {j\left( \frac{\omega_{e}^{2}{C_{b}\left( \omega_{e}^{2} \right)}}{\frac{1}{R_{el}^{2}} + \left( {\omega_{e}^{2}{C_{b}\left( \omega_{e}^{2} \right)}} \right)^{2}} \right)}}$Where

-   -   ω_(e) ¹=1^(st) electrical excitation Frequency    -   ω_(e) ²=2^(nd) electrical excitation Frequency    -   (4) Voltage (V) and Current (I) phasor relationship, with ω_(e)        ¹ and ω_(e) ²

$\frac{V\left. \sqrt{}\theta_{e}^{1} \right.}{I} = Z_{INT}^{1}$$\frac{V\left. \sqrt{}\theta_{e}^{2} \right.}{I} = Z_{INT}^{2}$Where;

-   -   θ_(e) ¹=Phase Angle difference between and I due to 1^(st)        electrical frequency excitation    -   θ_(e) ²=Phase Angle difference between V and I due to 2^(nd)        electrical frequency excitation

In Equation 4, there are two different complex internal impedancesresponses, Z_(INT) ¹ and Z_(INT) ². The battery responds differentlybecause it is being excited by a different electrical excitationfrequency and the resultant complex internal impedance response to eachis different. Some of the components that make up the battery's complexinternal impedance (Z_(INT)) present a different opposition to thevarious frequencies with which they are excited. The components thatmake up R_(m) (the metallic opposition, electrons) are not veryfrequency sensitive at the frequencies of interest. However, thecomponents that make up R_(el) (the electrochemical opposition, ions)are sensitive at all frequencies. Additionally, the capacitivecomponent, in FIG. 1, and its contribution to the complex impedanceresponse of the battery is also frequency sensitive. Thus, it should beclear, that the two expressions for Z_(INT) in Equation 4, Z_(INT) andZ² _(INT), will have a different response to different excitationfrequencies, ω₁ and ω₂ respectively. But, recall that the main problemwith the single frequency method was that the complex impedanceresponse, and it's resultant phase angle, was highly dependent on theage, SoC, temperature and various design, manufacturing tolerancesand/or process. So, in order for this approach to be effective, and toinstill confidence in this electronic battery SoH measurement technique,it would have to eliminate all of these dependencies so that theresultant measurement is truly indicative of the cell's age.

This measurement technique takes the difference of the resultant phaseangle response, θ_(e) ¹ and θ_(e) ², measured at the terminals of thebattery, and this provides additional insight in to the battery'sinternals and this aids in determining the true SoH of the battery. Onewould think that this two frequency approach is far superior to thesingle frequency approach; however, it is the intent of this disclosureto show otherwise. Just using two electrical excitation frequenciestaken close in time is not enough to make this method of measurementacceptable in the industry. There are other variations of this conceptthat have been explored, e.g. scanning through a wide range offrequencies and measuring several resultant responses, all of theelectrical excitation type. These attempts have merit but they are alsolimited and they too have several variations in the response which makethese measurements unreliable as well. The added scanning significantlycomplicates the required electronics and greatly raises the cost. Onemust keep in mind that the utility or end user is not going to pay morefor a battery monitoring system then the battery itself. This would notmake much business sense; why not just replace the battery when it issuspect. So, the goal is to eliminate the variation without complicatingthe required electronics and increasing the cost.

-   -   (5) The battery internal impedance difference ΔZ_(INT) based        on (3) is:

${\Delta\; Z_{INT}^{e}} = {{Z_{INT}^{e\; 1} - Z_{INT}^{e\; 2}} = {\left( {\frac{\frac{1}{R_{el}\left( \omega_{e}^{1} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{1} \right)} + \left( {\omega_{e}^{1}{C_{b}\left( \omega_{e}^{1} \right)}} \right)^{2}} - \frac{\frac{1}{R_{el}\left( \omega_{e}^{2} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{2} \right)} + \left( {\omega_{e}^{2}{C_{b}\left( \omega_{e}^{2} \right)}} \right)^{2}}} \right) - {{j\left( {\frac{\omega_{e}^{1}{C_{b}\left( \omega_{e}^{1} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{1} \right)} + \left( {\omega_{e}^{1}{C_{b}\left( \omega_{e}^{1} \right)}} \right)^{2}} - \frac{\omega_{e}^{2}{C_{b}\left( \omega_{e}^{2} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e}^{2} \right)} + \left( {\omega_{e}^{2}{C_{b}\left( \omega_{e}^{2} \right)}} \right)^{2}}} \right)}.}}}$

The impedance difference in Equation 5, although tedious, represents theadvantages of the dual electrical frequency approach. Most importantly,this complex impedance response does not contain R_(m) which drops outwhen taking this difference, and as will be recalled from the singlefrequency method description this term was present in the compleximpedance (Z_(int)) and added variability to the measured phase angle(θ_(e)). Only one component of R_(m), R_(gridpaste), was affected byage, but all the components of R_(m); R_(post), R_(alloy), R_(grid) andR_(gridpaste) were all affected by temperature and the battery design,manufacturing tolerance and/or process. Thus, eliminating this term fromthe complex impedance expression was a step in the right direction. Thatis, this dual frequency excitation difference method eliminated theeffects that two of the battery's conditions, i.e. temperature and thebattery, its design, manufacturing tolerance and/or processes, had onR_(m), and thus reduced this contribution to the variability of themeasurement.

By exciting the battery close in time and taking the difference of thephase response of two distinct electrical excitation frequencies two ofthe large contributors to the variation of the measurement have beeneliminated. Hence, the variability in this measurement technique hasbeen reduced, and closer approaches a measurement that is morerepresentative of the true SoH of the battery, its age. Essentially,since the temperature did not change and the battery design is the samebetween the two measurements their contribution to the variability inthe measurement is eliminated. FIG. 4 shows that the green shaded areain FIG. 3 above has been reduced by this dual frequency approach. Thered shaded area represents the variability that was removed byeliminating the effects of temperature and battery design, manufacturingtolerances and/or process on R_(m).

However, from Equation 5 it is shown that Z_(INT) is still dependent onR_(el), C_(b) and ω_(e). As described earlier, R_(el) is affected by thebattery's age, SoC, temperature and battery design, and manufacturingtolerances and/or processes. So even with this dual frequency excitationdifference approach there will still be significant variability in themeasurement and it is not all due to the battery's age. The main goal ofthe dual frequency approach was to eliminate the variation inmeasurement so that it better represented the true health of thebattery, however, in doing so, this measurement technique actually addedvariability into the measurement results. Since, the components thatmake up R_(el) will behave differently to different electricalexcitation frequencies this behavior manifests itself the differencemeasurement. Thus, new unknowns have been added to the measurementtechnique that were non-existent in the single electrical excitationtechnique. Therefore, the selection of the second excitation frequencyalone will yield different results in the measured phase angledifference, Δθ_(e).

It is clear that even though the dual frequency approach helped, and wassuperior to the single frequency approach, it still has limitations inits ability to accurately measure the SoH of a battery. The variationsinduced by different battery types and material, i.e. paste, separatorand electrolyte, aging, SoC, temperature, are still present within theΔZ_(INT) expression in Equation 5 and they are a direct result of thevariations in R_(el) and its frequency response to two distinctelectrical excitation frequencies.

It is worthy to note that much study and exploration has been expendedon the electrical frequency selection for this type of measurementmethod. From Equation 5 it is evident that the value of both ω_(e) ¹ andω_(e) ² will affect the phase difference, Δθ_(e). Meaning, if twoidentical batteries are tested and all other parameters remained equalone would get two different Δθ_(e), if one used two differently suppliedEIS equipment. This is not visible to the end-user because the equipmentmanufactures draw their own conclusions on what the actual SoH is basedon the phase difference response seen by their system. The real goal wasto reduce variability in the measurement of SoH, in order to get thetrue electrochemical health of the battery, now we have even furtheredthe level of variation: the EIS equipment supplier's selection of twoelectrical excitation frequencies. So, we eliminated some of thevariability of the single excitation technique but added somevariability based on our enhanced measurement technique. Thus, thistends to keep the green shaded area in FIG. 4 larger than it should be.Consequently, it is not surprising that one EIS vendor may say thattheir system is superior based on frequency selection, but, as we havedisclosed, all EIS equipment using this electrical measurement method issubject to the variations brought on by R_(el). Albeit, the variationmay be less from one frequency selection to the next, however, thisdifference is marginal at best. Certainly not a ‘real’ performancedifferentiator in the market place!

The Mechanical Excitation Frequency (ω_(m)) and Single ElectricalExcitation Frequency (ω_(e)) Method

As shown the single and dual electrical excitation frequency approachesboth have their advantages and disadvantages. The evolution of EIStechniques/technologies has grown in complexity and cost but theperformance, i.e. their ability to accurately measure SoH, has not grownin proportion. It is disclosed here that there is a much more accuratemethod for determining the actual SoH of a battery. The principle behindthis method is to introduce a mechanical excitation frequency ω_(m) asis disclosed in U.S. Pat. No. 7,592,094. This prior art demonstratesthat the introduction of a mechanical excitation frequency ω_(m) to anenergy storage device makes the device operate much more efficiently andwill substantially minimize the storage device's degradation. Thisdisclosure is focused on the advantages that mechanical excitation canadditionally have on one's ability to accurately determine the battery'strue SoH, its age. This adds value to the use of mechanical excitationin the energy storage market place, meaning, if the utility is takingadvantage of the performance and cycle life improvements that mechanicalexcitation offers then it makes commercial business sense to takeadvantage of this novel and industrious method of SoH determination. Thecombination of both mechanical excitation for improved performance andlife and a better and more accurate SoH measurement technique willchange the face of energy storage as we currently know it.

It will be demonstrated that the variations brought on by R_(el), in thesingle and dual electrical excitation frequency can be all buteliminated by the proper application of a mechanical excitationfrequency (ω_(m)). As discussed above, the expression for ΔZ_(INT) inEquation 5 was effected by the battery's SoC, temperature and variousdesign, manufacturing tolerances and/or process as well as the device'sage, i.e. SoH. When testing a string of batteries with the sameelectrical excitation measurement device, the user will get a differentΔθ_(e), i.e. SoH, reading for each battery in the string. The goal ofany measurement technique is to ensure that the measured Δθ_(e) isindicative of the battery's true SoH, and of that alone.

To illustrate, take a string of batteries and envision that we are goingto test each one individually. Each battery in the string will be at adifferent age, even if the string was comprised of batteries from thesame lot and placed into service at the same time. The problem is thateach battery cell charges and discharges at different rates throughoutits life and this is mainly due to differences in its internal impedance(Z_(INT)) and imbalances between cells in the string. These are the samedifferences that make the current electronic excitation means ofdetermining the batteries true SoH very inaccurate and unreliable.Therefore, each cell will be at a different cycle life, a.k.a. age.Often, one confuses cycle life with calendar life but thedifferentiation is critical.

Since it was already determined that R_(el)'s magnitude is sensitive toaging mechanisms, part of each cell's complex impedance response to anelectrical excitation frequency, and the corresponding Δθ_(e), is due toage. The question is how much of the measured phase difference can beattributed to age? After all, this is what everyone is looking for sincethe battery's true SoH is, or more correctly, should be, a measure ofits electrochemical health, e.g. its ability to convert chemicalpotential energy to electrical energy then back again. So, what wereally want to know is how the paste, separator and electrolyte willinteract, i.e. the energy conversion process, when called upon forservice. The effects from the battery's SoC, temperature, and design,manufacturing tolerance and/or process should not be present in themeasurement. Even though these parameters play a part in what thebattery will supply, i.e. capacity-Ahrs, for its given state, one shouldnot mislead one into prematurely replacing a battery pack based on thevariability they add to the chosen measurement technique. All we reallywant in the measurement result are the effects that are due to thebattery's age! R_(el)'s magnitude in response to an electricalexcitation frequency, or the difference in the response from twoelectrical excitation frequencies, alone is descriptive, but it is alsovery deceiving and this inherent uncertainty directly effects autility's bottom line, i.e. cost! Clearly, if a battery pack's SoH is inquestion based on the results of the applied measurement technique thenthis will drive the utility to performing a costly and operationalrestrictive test discharge which, as explained earlier, actuallydetracts from the battery pack's useful life. Therefore, the purpose ofthis novel, inventive and industrious mechanical excitation technique isto remove this inherent uncertainty in the electronic measurementtechnique, thereby, obviating the need to conduct frequent and costlytest discharges.

R_(el) is comprised of three components; R_(Paste), R_(Sep) andR_(electrolyte), their individual magnitude response to an electricalexcitation frequency will be analyzed below:

-   -   1. R_(Paste), R_(Sep), R_(electrolyte) and C_(b) are sensitive        to aging, thus adding variability to resultant Δθ_(e)    -   2. R_(paste) and R_(electrolyte) are sensitive to temperature,        thus adding variability to resultant Δθ_(e)        -   a. As discussed earlier R_(Sep) could be sensitive to            temperature, but in general, in most practical            circumstances, it is not in the temperature range of            interest.    -   3. R_(electrolyte), R_(Paste) and C_(b) are sensitive to SoC,        thus adding variability to resultant Δθ_(e)    -   4. R_(Paste), R_(Sep), R_(electrolyte) and C_(b) are susceptible        to battery material and manufacturing tolerances and/or process,        thus adding variability to resultant Δθ_(e)

Thus as can be seen each of these component's magnitude response to anelectrical excitation frequency are impacted by the conditions notedabove, thus adding to the variability of the resultant measured phaseangle θ_(e). Therefore the true effects of aging on the electrochemicalhealth of the battery, i.e. SoH, are masked by the effects oftemperature, SoC and the battery design, manufacturing tolerances and/orprocesses. It is also subject to the EIS equipment design and tolerancesas well as this equipment supplier's interpretation of the electricalexcitation measured response.

By measuring the internal impedance with and without a mechanicalexcitation frequency (ω_(m)) and only using a single electricalexcitation frequency (ω_(e)) the influences of the temperature, SoC andbattery design, manufacturing tolerances and/or processes on themeasured phase angle θ_(e) can be eliminated and the resultant measuredθ_(e) will be indicative of the true electrochemical health, i.e. SoH(age), of the battery. This mechanical measurement technique alsoreduces the response's susceptibility to the EIS equipment design andtolerance and substantially reduces variance introduced by thedesigner's interpretation of the result measured response.

-   -   (6) Battery Internal impedance difference, with ω_(e) and ω_(m),        ΔZ_(INT) ^(ω) ^(e) (ω_(m)), compare to equation (5) in which        both applied frequencies are electrical.

${\Delta\;{Z_{INT}^{\omega_{e}}\left( \omega_{m} \right)}} = {{Z_{INT}^{\omega_{e}} - {Z_{INT}^{\omega_{e}}\left( \omega_{m} \right)}} = {\left( {\frac{\frac{1}{R_{el}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} - \frac{\frac{1}{R_{el}\left( \omega_{m} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{m} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}} \right) - {j\left( {\frac{\omega_{e}{C_{b}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} - \frac{\omega_{e}{C_{b}\left( \omega_{m} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{m} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}} \right)}}}$Constraints on Electrical Excitation

$\begin{matrix}{\left( {\omega_{e}C_{b}} \right)^{2}\operatorname{>>}{\frac{1}{R_{el}^{2}}\mspace{14mu}{and}\mspace{14mu}\left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}\operatorname{>>}\frac{1}{R_{el}^{2}\left( \omega_{m} \right)}} & (7)\end{matrix}$

Equation 6 can be manipulated and transformed by using constraintssimilar to that shown in in Equation 7. One should keep in mind thatthere are other constraints on electrical excitation frequency selectionthat have been learned and applied by EIS equipment suppliers overdecades of use and that these should also be considered during theimplementation of this disclosed measurement technique. The mechanicalexcitation frequency selection is dependent on electrochemicalconstraints, i.e. chemical reactions and battery chemistry, which willbe discussed later in this disclosure. The Z_(INT) expression inEquation 6 represents the battery's complex internal impedance andreveals its dependency on both the electrical and mechanical excitationfrequency. Equation 8 and 9 below represent the polar form of thebattery's internal impedance (Z_(INT)) and are used for illustrativepurposes, and show that the resultant magnitude of Z_(INT) and theresultant phase shift θ_(e) between V and I is different when mechanicalexcitation ω_(m) is applied while taking a single electrical frequencymeasurement. The phase shift θ_(e) (Equation 8) is a result ofelectrical excitation and it is dependent on the mechanical excitationω_(m) (Equation 9). The differences in the phase shift ω_(e) with andwithout mechanical excitation are due to the contributions of R_(el) andC_(b) in Equation 6 above.Z_(INT) ^(ω) ^(e) ∠θ^(e) without mechanical excitation  (8)Z_(INT) ^(ω) ^(e) (ω_(m))∠θ^(e)(ω_(m)) with mechanical excitation  (9)

This difference expression for Z_(INT), with and without mechanicalexcitation, reveals very pertinent electrochemical health informationabout the battery. From FIG. 5 the difference from the single electricalexcitation phase response, and the single electrical excitation phaseresponse with mechanical frequency excitation (the red shaded area), canbe used to better ascertain the true SoH of the battery (the greenshaded area). Essentially, this phase difference is with and withoutmechanical excitation is measured, and the resultant difference (greenshaded area) is indicative of the electrochemical health of the battery.

The green shaded area (above the horizontal axis) in FIG. 5 does nothave the variability that plagued the single electrical excitationmethod with the exception of that induced by the age of the device.These measurements are taken very closely in time in an environment inwhich the temperature is held substantially constant, therefore,temperature does not affect the change in the magnitude response ofR_(el) with and without mechanical excitation, SoC does not affect thechange in the magnitude response of R_(el) with and without mechanicalexcitation, and, finally the battery design, manufacturing tolerancesand/or processes do not affect the change in magnitude response ofR_(el) with and without mechanical excitation. These variability's arerepresented by the red shaded area (below the horizontal axis) in FIG.5. All that affects the magnitude of R_(el) in this measurementtechnique is the effect of the mechanical excitation signal (ω_(m)) onthe opposition to the flow of energy. Therefore, the battery's internalcomplex impedance response is not only dependent on the electricalexcitation frequency (ω_(e)) it is also a function of the mechanicalexcitation frequency (ω_(m)).

By applying mechanical energy at the proper frequency and amplitude thekinetic transport deficiencies of the reaction ions are mitigated. Theresult is a reduction in R_(el) and this in turn will impact the compleximpedance response and corresponding phase angle. This reduction inR_(el) is at the electrode-electrolyte interface and it is mainly due tothe R_(paste) and R_(electrolyte) contribution. This is accomplished bythe interaction of the mechanical wave and the subsequent altering oflimiting pore sizes that are formed within the insulator layer (PbSO₄)that is found all over the electrode reaction area during discharge. Themechanical waveform is at a frequency which ensures that the poredimensions are kept large enough to allow/ensure passage of the largerand less energetic reaction product ions (HSO₄ ⁻ and SO₄ ⁻⁻) so thattheir concentration levels and corresponding ionic fluxes are generallyhigher and they are more able to rapidly change, at distances that arecloser to the electrode surface, in response to changes in the Pb⁺⁺ ionflux (which are based on electrode potential changes). If the mechanicalenergy does not reduce R_(el) then the electrochemical health of thecell is in question. As the battery ages the effects of mechanicalenergy on the magnitude of R_(el) will slowly diminish overtime, andwill result in less of an impact on the battery's complex impedanceresponse and therefore less of a change in the resultant phase angle.

It should also be seen that the variance introduced by the EIS equipmentitself has been eliminated from the resultant complex impedance responseand thus does not contribute to the variability in this measurementtechnique, as long as the electrical excitation frequency selection issufficient so that the constraints illustrated in Equation 7 hold true.

The only thing that will influence the change in the magnitude responseof R_(el) is the predetermined mechanical excitation signal. In thismeasurement technique the only variability introduced will be due to theeffects of aging on R_(el) and C_(b). This is the goal of any EISmeasurement technique.

True State-of-Health (SoH) Measurement Using Single Electrical (ω_(e))and Mechanical (ω_(m)) Frequency Excitation Technique

Since the variability in the single electrical frequency technique waseliminated by applying a mechanical excitation frequency, a simple andstraightforward measurement of the true SoH of the battery is nowpossible. However, it should be understood that many differentalgorithms' and prediction models can be employed based on thisdisclosure. The underlying premise that makes these other modelingalgorithms' and prediction methods deployable is that the application ofmechanical excitation energy has provided additional information on thetrue electrochemical health of the electrochemical energy storage and/orenergy conversion device. This measure is indicative of the battery'strue electrochemical health and this will give the battery user reliableand unquestionable information about the battery's health, its age. Theonly change in the phase angle Δθ_(e) returned while the battery isunder the influence of the proper mechanical excitation energy will bedue to the battery components that are susceptible to aging phenomenon.As the battery ages these battery components will be less and lesssusceptible to the effects of the applied mechanical energy and theelectrical phase change based on this mechanical excitation will becomeless and less prominent, i.e., Δω_(e)(ω_(e))−Δθ_(e)(ω_(m))→0.Essentially, the green shaded area (above the horizontal axis) in FIG. 5will get larger and larger as the battery undergoes aging phenomenon,with Δθ_(e)(ω_(m))→Δθ_(e)(ω_(e)). The magnitude of this phase anglechange Δθ_(e)(ω_(m)), when mechanical excitation (ω_(m)) is applied, isdependent only on the contributions of the battery components,R_(paste), R_(Sep), R_(electrolyte), and C_(b). As these components age,the mechanical energy (θ_(m)) will not have such a pronounced effect ontheir contributions to this electrical phase change Δθ_(e)(ω_(m)), andthis will be indication that the electrochemical health of the batteryis declining. A measurement of the Δθ_(e)(ω_(m)), while mechanicalexcitation (ω_(m)) is applied, will be the basis that all futuremeasurements will be compared to. If at some future time in thebattery's life, the measured Δθ_(e)(ω_(m)), while mechanical excitation(c)_(m)) is applied, is less than that of the previous measurement, thenthis difference is due to battery aging only. Eventually, when thebattery is heavily aged, or near end of life, the mechanical excitationenergy will not change the electrical phase angle ω_(e), i.e., thedifference between these two phase differencesΔθ_(e)(ω_(e))−Δθ_(e)(ω_(m))→0, and the battery pack, and/or cell, shouldbe replaced.

Since the aging effect of the battery components in question willgradually reduce their respective contributions to the battery'sinternal complex impedance response, and correspondingly change themeasured phase angle ω_(e), one can take measurements at predeterminedtimes, chart the progression in the phase angle change, and actuallypredict when the battery, and/or cell, will reach the end of its usefullife. In fact, if one knows the actual SoH of the device under test onecan apply a SoH factor to a known SoC and be able to determine theavailable capacity of that energy storage device and/or the conversionefficiency of an energy conversion device. It should also be understoodthat the variability introduced by the majority of the battery'scomponents in the single electrical frequency technique can also stillyield useful information on the overall health of the battery.

Several different and useful variations of this prediction model can beincorporated, and this will then aid the battery user in makingdecisions about their battery pack's health and when imminentreplacement is necessary. Several phase angle θ_(e)(ω_(m)) measurements,while mechanical excitation (ω_(m)) is applied, are taken and aprojection of remaining battery life is determined. In one non-limitingembodiment of this disclosure, the age related contributions areprojected using a straight-line approximation method and a prediction onremaining battery life is determined. Using various predictionsalgorithms and prediction techniques this method and device can also beused to accurately predict the device's residual energy capacityavailable for use as well as the device's remaining life time. Whileonly the SoH determination method is described in this disclosure, itshould be understood that the underlying premise of the measurement andprediction technique disclosed here is based on the availability ofadditional electrochemical health information that is made possible withthe use of mechanical excitation energy with the current, and future,electrical excitation only measurement techniques, whether it be singlefrequency, dual, scanning, etc.

As a non-limiting example, FIG. 6 is the straight-line approximationmethod for a typical battery. Let us say for illustrative, non-limitingnumbers, that when a given battery is new, a battery is tested, and as abaseline, it is established that Δθ≡Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m))=80°.Over time as the battery ages, this 80° will diminish, which is to say,Δθ_(e)−Δθ_(e)(ω_(m)) will trend downward toward zero. AsΔθ≡Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m))→0°, this means that the battery isapproaching it end of life. While the actual state of health may not beperfectly linear as illustrated in FIG. 6, i.e., while aΔθ_(e)−Δθ_(e)(ω_(e))=40° reading which is halfway between 0° end of lifeand the 80° baseline may not mean that the battery is at exactly 50% ofits useful life (i.e., while the straight, negatively-sloped line inFIG. 6 may not be exactly a line), one may use the linear scale in FIG.6 as a good first order approximation of remaining battery life. FIG. 6is analogous, then, to the indicator in an automobile which showsroughly the proportion of gasoline which remains in the tank. However,Δθ=Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m))→0° is in all cases the measurement thatindicates actual end of battery life, so the magnitude ofΔθ_(e)(ω_(e))−Δθ_(e)(ω_(m)) in relation to a baseline-time phasedifference (such as the 80° example above) may be taken as a roughlinear gauge of battery SoH.

The knowledge possessed by someone of ordinary skill in the art at thetime of this disclosure is understood to be part and parcel of thisdisclosure and is implicitly incorporated by reference herein, even ifin the interest of economy express statements about the specificknowledge understood to be possessed by someone of ordinary skill areomitted from this disclosure. While reference may be made in thisdisclosure to the invention comprising a combination of a plurality ofelements, it is also understood that this invention is regarded tocomprise combinations which omit or exclude one or more of suchelements, even if this omission or exclusion of an element or elementsis not expressly stated herein, unless it is expressly stated hereinthat an element is essential to applicant's combination and cannot beomitted. It is further understood that the related prior art may includeelements from which this invention may be distinguished by negativeclaim limitations, even without any express statement of such negativelimitations herein. It is to be understood, between the positivestatements of applicant's invention expressly stated herein, and theprior art and knowledge of the prior art by those of ordinary skillwhich is incorporated herein even if not expressly reproduced here forreasons of economy, that any and all such negative claim limitationssupported by the prior art are also considered to be within the scope ofthis disclosure and its associated claims, even absent any expressstatement herein about any particular negative claim limitations.

Finally, while only certain preferred features of the invention havebeen illustrated and described, many modifications, changes andsubstitutions will occur to those skilled in the art. It is, therefore,to be understood that the appended claims are intended to cover all suchmodifications and changes as fall within the true spirit of theinvention.

I claim:
 1. A method for testing the state-of-health of anelectrochemical energy device, comprising: applying electricalexcitations to the energy device at a predetermined electricalexcitation frequency ω_(e); applying mechanical excitations to theenergy device at a predetermined mechanical excitation frequency ω_(m);measuring an electrically-induced phase difference Δθ_(e)(ω_(e)) betweenvoltage (V) and current (I) within the energy device from applying saidelectrical excitations; measuring a mechanically-induced phasedifference Δθ_(e)(ω_(m)) between voltage (V) and current (I) within theenergy device from applying said mechanical excitations; and deducingthe state-of-health of said energy device by comparing saidelectrically-induced phase difference Δθ_(e)(ω_(e)) with saidmechanically-induced phase difference Δθ_(e)(ω_(m)).
 2. The method ofclaim 1, further comprising: taking a differenceΔθ=Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m)) between said electrically-induced phasedifference Δθ_(e) and said mechanically-induced phase differenceΔθ_(e)(ω_(m)); and using said difference as a basis to deduce said SoH.3. The method of claim 2, further comprising: deducing thestate-of-health of said energy device by determining a magnitude ofΔθ=Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m)) in relation to 0°, wherein betterstate-of-health is deduced from said magnitudes being larger and poorerstate-of-health is deduced from said magnitudes being smaller.
 4. Themethod of claim 2, further comprising: deducing that said energy deviceis approaching its end of life by determining thatΔθ=Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m))→0°.
 5. The method of claim 1, furthercomprising: at a baseline time, determining baseline-time phasedifferences Δθ_(e)(ω_(e)) and Δθ_(e)(θ_(m)) between current and voltageof said energy device; at a later time, determining later-time phasedifferences Δθ_(e)(ω_(e)) and Δθ_(e)(θ_(m)) between current and voltageof said energy device; and deducing said state of health by comparingsaid later-time phase difference with said baseline-time phasedifference.
 6. The method of claim 5, further comprising: deducing saidstate of health by determining how much said later-time phase differencehas diminished from said baseline time phase difference.
 7. The methodof claim 6, further comprising deducing a magnitude of decline in saidstate of health substantially in proportion to said diminution.
 8. Themethod of claim 1, wherein: a difference between measurements ofinternal impedance Z_(INT) the energy device when said electricalexcitation frequency ω_(e) is applied versus when said mechanicalexcitation frequency ω_(m) is applied, is determined according to:${{{Z_{INT}^{e}\left( \omega_{e} \right)} - {Z_{INT}^{e}\left( \omega_{m} \right)}} = {\left( {\frac{\frac{1}{R_{el}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} - \frac{\frac{1}{R_{el}\left( \omega_{m} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{m} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}} \right) - {j\left( {\frac{\omega_{e}{C_{b}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} - \frac{\omega_{e}{C_{b}\left( \omega_{m} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{m} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}} \right)}}},$where R_(el) designates an electrochemical resistance of said energydevice and C_(b) designates a storage capacity of said 7 energy device;further comprising: deducing said electrically-induced phase differenceΔθ_(e)(θ_(e)) between said voltage V and said current I according to${{Z_{INT}^{e}\left( \omega_{e} \right)} = \frac{V\left. \sqrt{}{\theta_{e}\left( \omega_{e} \right)} \right.}{I}};$and deducing said mechanically-induced phase difference Δθ_(e)(ω_(m))between said voltage V and said current I according to${Z_{INT}^{e}\left( \omega_{m} \right)} = {\frac{V\left. \sqrt{}{\theta_{e}\left( \omega_{m} \right)} \right.}{I}.}$9. A apparatus for testing the state-of-health of an electrochemicalenergy device, comprising: an electrical excitation source for applyingelectrical excitations to the energy device at a predeterminedelectrical excitation frequency ω_(e); a mechanical excitation sourcefor applying mechanical excitations to the energy device at apredetermined mechanical excitation frequency ω_(m); a measurementdevice for measuring an electrically-induced phase differenceΔθ_(e)(ω_(m)) between voltage (V) and current (I) within the energydevice from applying said electrical excitations; and said measurementdevice for further measuring a mechanically-induced phase differenceΔθ_(e)(ω_(m)) between voltage (V) and current (I) within the energydevice from applying said mechanical excitations; wherein thestate-of-health of said energy device is deduced by comparing saidelectrically-induced phase difference Δθ_(e)(ω_(e)) with saidmechanically-induced phase difference Δθ_(e)(ω_(m)).
 10. The apparatusof claim 9, wherein: the state-of-health of said energy device isdeduced by taking a difference Δθ=Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m)) betweensaid electrically-induced phase difference Δθ_(e) and saidmechanically-induced phase difference Δθ_(e) (ω_(m)).
 11. The apparatusof claim 10, wherein: the state-of-health of said energy device isdeduced by determining a magnitude of Δθ=Δθ_(e)(ω_(e))−Δ_(e)(ω_(m)) inrelation to 0°, and wherein better state-of-health is deduced from saidmagnitudes being larger and poorer state-of-health is deduced from saidmagnitudes being smaller.
 12. The apparatus of claim 10, wherein: saidenergy device is approaching its end of life is deduced by determiningthat Δθ=Δθ_(e)(ω_(e))−Δθ_(e)(ω_(m))→0°.
 13. The apparatus of claim 9,wherein: baseline-time phase differences Δθ_(e) (ω_(e)) andΔθ_(e)(ω_(m)) between current and voltage of said energy device aredetermined at a baseline time; later-time phase differencesΔθ_(e)(ω_(e)) and Δθ_(e)(ω_(m)) between current and voltage of saidenergy device are determined at a later time; said baseline-time phasedifference is compared with said later-time phase difference to deducesaid state-of-health.
 14. The apparatus of claim 13, wherein: said stateof health is deduced by determining how much said later-time phasedifference has diminished from said baseline time phase difference. 15.The apparatus of claim 14, wherein a magnitude of decline in said stateof health is deduced substantially in proportion to said diminution. 16.The apparatus of claim 9, wherein: a difference between measurements bysaid measurement device of internal impedance Z_(INT) the energy devicewhen said electrical excitation frequency ω_(e) is applied versus whensaid mechanical excitation frequency ω_(m) is applied, is determinedaccording to:${{{Z_{INT}^{e}\left( \omega_{e} \right)} - {Z_{INT}^{e}\left( \omega_{m} \right)}} = {\left( {\frac{\frac{1}{R_{el}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} - \frac{\frac{1}{R_{el}\left( \omega_{m} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{m} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}} \right) - {j\left( {\frac{\omega_{e}{C_{b}\left( \omega_{e} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{e} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{e} \right)}} \right)^{2}} - \frac{\omega_{e}{C_{b}\left( \omega_{m} \right)}}{\frac{1}{R_{el}^{2}\left( \omega_{m} \right)} + \left( {\omega_{e}{C_{b}\left( \omega_{m} \right)}} \right)^{2}}} \right)}}},$where R_(el) designates an electrochemical resistance of said energydevice and C_(b) designates a storage capacity of said energy device;said electrically-induced phase difference Δθ_(e)(ω_(e)) between saidvoltage V and said current I is deduced according to${{Z_{INT}^{e}\left( \omega_{e} \right)} = \frac{V\left. \sqrt{}{\theta_{e}\left( \omega_{e} \right)} \right.}{I}};$and said mechanically-induced phase difference Δθ_(e)(ω_(m)) betweensaid voltage V and said current I is deduced according to${Z_{INT}^{e}\left( \omega_{m} \right)} = {\frac{V\left. \sqrt{}{\theta_{e}\left( \omega_{m} \right)} \right.}{I}.}$